Hierarchical DPT mask planning for contact layer

LELE/LFLE based double patterning (DPT) with ArF water-based immersion systems has emerged as a strong candidate to first extend lithography to 32nm and below. Mask planning for DPT consists of conflict visualization when design is not manufacturable with DPT and mask assignment either when it is or despite it is not. Concurrent with the advancements in double patterning process, there has been active research [1] [2] [3] [4] addressing the problem of mask planning. As geometries across the chip can potentially involve in the same conflict, DPT decomposition has been recognized as unbounded [5] [4]. We will show in this paper that the unbounded nature of a potential conflict drawing in geometries from across the chip, however, poses little obstacle to efficient conflict visualization or mask assignment. Hierarchy already present in design offers different levels of abstraction for conflicts spanning across various levels of the hierarchy. And pseudo hierarchy from tiles of fully flattened design are even more amenable in that they are already positioned with respect to the flat view, and tiles overlap only marginally when they do. While there have been ample research literature in the mask assignment problem with respect to geometries within cell or flat view of a design, not much have been published on how hierarchy is addressed or any special handling needed for peculiar complexities arising from the presence of hierarchy [5] [6]. Hierarchy adds a subtle but significant dimension to the mask planning problems. This paper investigates contact layer mask planning for DPT, and presents results on two new problems due to hierarchical processing.